The British Future study, based on a survey of more than 3,600 people, suggested concern with immigration numbers is focused primarily on low-skilled migration.

Nearly two in three respondents (64%), including 50% of Remain voters, expressed a preference for a reduction in immigration from the EU for low-skilled workers.

Mr Katwala said: "There is public support, across political and referendum divides, for an immigration system that combines the UK control demanded in the referendum with openness to the migration that our economy will continue to need."